标题： 路径积分形式的玻色型马尔可夫开放量子动力学，使用蒙特卡罗随机轨迹的Glauber-Sudarshan P、Wigner和Husimi Q函数及混合方法 显示英文标题

标题： Path-Integral Formulation of Bosonic Markovian Open Quantum Dynamics with Monte Carlo stochastic trajectories using the Glauber-Sudarshan P, Wigner, and Husimi Q Functions and Hybrids

摘要： 基于准概率的随机微分方程（SDEs）的蒙特卡罗（MC）轨迹采样，如Glauber-Sudarshan P、Wigner和Husimi Q函数，使我们能够研究由Gorini-Kossakowski-Sudarshan-Lindblad（GKSL）方程描述的玻色子开放量子多体动力学。在此方法中，初始分布和随机噪声的MC采样包含量子涨落，因此我们可以超越平均场近似。然而，仅当对应的福克-普朗克方程具有半正定扩散矩阵时，才能使用SDEs进行描述。在本工作中，我们独立于福克-普朗克方程（FPE）的推导，通过路径积分公式解析地推导了任意哈密顿量和跃迁算符的SDEs。在推导过程中，我们利用$s$序的准概率，构建了GKSL方程的路径积分表示，通过改变实参数$s$，系统地描述了上述准概率。该推导的关键点是我们采用了路径积分中的Hubbard-Stratonovich（HS）变换，但其应用并不总是可行的。我们发现HS变换的可行条件与FPE中扩散矩阵的半正定性条件相同。在基准计算中，我们确认所得到的SDE的MC模拟能够很好地再现数值可解模型中物理量和非等时关联函数的精确动力学，包括Bose-Hubbard模型。本工作明确了近似的适用性，并给出了系统且简化的获取可数值求解的SDEs的步骤。 显示英文摘要

摘要： The Monte Carlo (MC) trajectory sampling of stochastic differential equations (SDEs) based on the quasiprobabilities, such as the Glauber-Sudarshan P, Wigner, and Husimi Q functions, enables us to investigate bosonic open quantum many-body dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In this method, the MC samplings for the initial distribution and stochastic noises incorporate quantum fluctuations, and thus, we can go beyond the mean-field approximation. However, description using SDEs is possible only when the corresponding Fokker-Planck equation has a positive-semidefinite diffusion matrix. In this work, we analytically derive the SDEs for arbitrary Hamiltonian and jump operators based on the path-integral formula, independently of the derivation of the Fokker-Planck equation (FPE). In the course of the derivation, we formulate the path-integral representation of the GKSL equation by using the $s$-ordered quasiprobability, which systematically describes the aforementioned quasiprobabilities by changing the real parameter $s$. The essential point of this derivation is that we employ the Hubbard-Stratonovich (HS) transformation in the path integral, and its application is not always feasible. We find that the feasible condition of the HS transformation is identical to the positive-semidefiniteness condition of the diffusion matrix in the FPE. In the benchmark calculations, we confirm that the MC simulations of the obtained SDEs well reproduce the exact dynamics of physical quantities and non-equal time correlation functions of numerically solvable models, including the Bose-Hubbard model. This work clarifies the applicability of the approximation and gives systematic and simplified procedures to obtain the SDEs to be numerically solved.